The Wales international scored the winner against Macedonia last weekend and made the difference again on Saturday as the Addicks avoided making their worst start to a campaign in more than seven years.
It was their second consecutive win at the Lancashire ground - and a first victory in seven attempts.
Gary Bowyer made two changes to the side that lost at Wigan. Scott Dann returned from injury and came in for the suspended Grant Hanley while the injured Corry Evans was replaced by Ben Marshall.
Charlton boss Chris Powell made two alterations of his own, with Bradley Pritchard and former Blackburn loanee Cameron Stewart in for Mark Gower and Callum Harriott.
The visitors had scored only once in their previous four games prior to the Ewood clash but almost ended that rotten run after five minutes when Church's effort was deflected wide.
The Wales striker made no mistake two minutes later, though, with a beautifully taken finish. Dale Stephens' chipped pass found Church, who controlled with his chest before slotting past Jake Kean with a controlled side-foot volley.
Charlton were indebted to Ben Hamer after 25 minutes when he produced a brilliant fingertip save after Leon Best had set up Jordan Rhodes on the edge of the area. His volley was heading for the corner but Hamer was there to thwart him.
Bowyer's side began to apply the pressure as the half wore on and, after Hamer elected to punch away a Tommy Spurr cross, Best ought to have scored. Jason Lowe nodded the ball into his path, but he could only blaze over from inside the area.
Blackburn had notched up 10 goals in five home games before Saturday and thought they had got an 11th after 60 minutes. Tom Cairney's corner was cleared as far as Lowe, who controlled before unleashing a brilliant volley that deflected just wide of the right post with Hamer scrambling.
But Church and Charlton could and maybe should have had a second moments later when the forward met Pritchard's drilled cross but his bullet header went straight into the grateful arms of Kean.
As the game progressed, Blackburn pegged the visitors back to the point that they had no players in the Rovers half at times but the home side struggled to test Hamer and Cairney's wild and misdirected effort on 79 minutes summed up the frustration.
Despite six minutes of stoppage time ensured a tense finish, but the visitors held on to claim three points - exactly 1,000 days since Powell's first win as Charlton boss.